Test of Randomness of Residuals for Modified Gompertz Model used for Modelling the Growth of Callus Cultures from Glycine wightii (Wight & Arn.) Verdc.

  • Shukor . M.S. Department of Biochemistry UPM


One of the most important preliminary investigations of callus attributes is the growth characteristics. Most often than not, callus growth curve is sigmoidal in characteristics. Frequently, plant scientists studying callus growth neglect the utilization of mathematical growth that are useful in obtaining important growth constants such as lag period, maximum specific growth rate and maximum growth or asymptote. Formerly, we model callus growth of Glycine wightii from published literature to obtain vital growth constants. We discovered that themodified Gompertz model via nonlinear regression utilizing the least square method was the best to explain the growth curve. Nevertheless, an important thing to consider, that has not been stated more than enough, is the residual of the model needs to be random. To make sure that randomness being fulfilled we carry out the Wald-Wolfowitz runs test. The results demonstrated that the number of runs was 5, and the expected number of runs within the assumption of randomness was 5, suggesting the series of residuals had perfect runs. The p-value obtained was higher than 0.05, hence the null hypothesis is not rejected suggesting no persuading proof of nonrandomnessof the residuals plus they do stand for noise.


[1] Ibrahim R, Hussein S, Noordin N, Azlan E, Manan MA, Adrian
H, et al. Advanced cell culture technology for essential oil
production and microarray studies leading to discovery of genes
for fragrance compounds in Michelia alba (Cempaka putih). Acta
Hortic. 2008;765:95–100.
[2] Hussein S, Ling APK, Ng TH, Ibrahim R, Paek KY.
Adventitious roots induction of recalcitrant tropical woody plant,
Eurycoma longifolia. Romanian Biotechnol Lett.
[3] Tokita N, Shimojo M, Masuda Y. Amino acid profiles of tropical
legumes, cooper (Glycine wightii), Tinaroo (Neonotonia wightii)
and Siratro (Macroptilium atropurpureum), at pre-blooming and
blooming stages. Asian-Australas J Anim Sci. 2006;19(5):651–4.
[4] Hammatt N, Nelson RS, Davey MR. Plant regeneration from
seedling explants of perennial Glycine species. Plant Cell Tissue
Organ Cult. 1987;11(1):3–11.
[5] Pandey P, Bansal YK. Plant regeneration from leaf and
hypocotyl explants of Glycine wightii (W. and A.) Verdc. var
longicauda. Jpn J Breed Tokio. 1992;42:1–5.
[6] Kiong ALP, Then CN, Hussein S. Callus induction from leaf
explants of Ficus deltoidea Jack. Int J Agric Res. 2007;2(5):468–
[7] Silva ALC da, Caruso CS, Moreira R de A, Horta ACG. Growth
characteristics and dynamics of protein synthesis in callus
cultures from Glycine wightii (Wight & Arn.) Verdc. Ciênc
E Agrotecnologia. 2005;29(6):1161–6.
[8] Razali NM, Wah YB. Power comparisons of Shapiro–Wilk,
Kolmogorov– Smirnov, Lilliefors and Anderson–Darling tests. J
Stat Model Anal. 2011;2:21–3.
[9] Jarque CM, Bera AK. Efficient tests for normality,
homoscedasticity and serial independence of regression residuals:
Monte Carlo evidence. Econ Lett. 1981;7(4):313–8.
[10] Snedecor GW, Cochran WG. Statistical methods. 7th ed. Ames
Iowa: Iowa State University Press; 1980.
[11] Motulsky HJ, Ransnas LA. Fitting curves to data using nonlinear
regression: a practical and nonmathematical review. FASEB J
Off Publ Fed Am Soc Exp Biol. 1987;1(5):365–74.
[12] Draper NR, Smith H. Applied Regression Analysis. Wiley, New
York; 1981.
[13] Rohatgi,..A..WebPlotDigitizer.http://arohatgi.info/WebPlotDigiti
zer/app/ Accessed June 2 2014.;
[14] Halmi MIE, Shukor MS, Johari WLW, Shukor MY. Evaluation
of several mathematical models for fitting the growth of the algae
Dunaliella tertiolecta. Asian J Plant Biol. 2014;2(1):1–6.
[15] Huitema BE, McKean JW, Zhao J. The runs test for
autocorrelated errors: unacceptable properties. J Educ Behav
Stat. 1996;21(4):390–404.
How to Cite
M.S., Shukor .. Test of Randomness of Residuals for Modified Gompertz Model used for Modelling the Growth of Callus Cultures from Glycine wightii (Wight & Arn.) Verdc.. Asian Journal of Plant Biology, [S.l.], v. 3, n. 1, p. 11-13, mar. 2016. ISSN 2289-5868. Available at: <http://journal.hibiscuspublisher.com/index.php/AJPB/article/view/267>. Date accessed: 21 sep. 2018.